Vincent had some pens. He gave ³₄ of his pens to Justin and bought 4 new pens. After that, he gave ²₅ of his remaining pens to his sister and bought another 7 new pens. In the end, Vincent had 34 pens.

1. How many pens did Vincent give to his sister?
2. How many pens did Vincent have at first?

(a)
Fraction of  his remaining pens after he gave to his sister
= 1 - ²₅
= ³₅

³₅ of his remaining pens = 34 - 7 = 27
¹₅ of his remaining pens = 27 ÷ 3 = 9
²₅ of his remaining pens = 2 x 9 = 18

Number of pens that Vincent gave to his sister = 18

(b)
⁵₅ of his remaining pens = 5 x 9 = 45

Fraction of his total pens after he gave to Justin
= 1 - ³₄
= ¹₄

¹₄ of his total pens = 45 - 4 = 41
⁴₄ of his total pens = 4 x 41 = 164

Number of pens that Vincent had at first = 164 

Answer(s): (a) 18; (b) 164